Volatility Forecasting & Economic Value

A Multi-Horizon Comparison of Rolling, EWMA and GARCH Models

---

1. Introduction

Volatility is a central object in quantitative finance.
It drives:

• Risk management
• Portfolio allocation
• Derivatives pricing
• Volatility targeting strategies

Financial returns exhibit well-known stylized facts:

• Volatility clustering
• Heavy tails
• Persistence
• Low autocorrelation of returns
• High autocorrelation of squared returns

The objective of this project is to:

1. Build a clean volatility forecasting pipeline
2. Compare multiple models:
   • Rolling volatility
   • EWMA (RiskMetrics)
   • GARCH(1,1)
3. Evaluate forecasts statistically using:
   • MAE
   • MSE
   • QLIKE
4. Evaluate economic value via a volatility targeting strategy
5. Analyze dynamics through interactive 3D volatility surfaces

We work in a multi-horizon setting (1, 5, 10 days) and annualize all volatility measures for consistency.

The goal is not only to identify the best statistical model, but to understand:

Does better volatility forecasting translate into better portfolio performance?

# --- Core imports ---
import sys
from pathlib import Path

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import plotly.io as pio

pio.renderers.default = "notebook_connected"

# --- Make src/ importable ---
ROOT = Path.cwd().resolve()
PROJECT_ROOT = ROOT.parent if ROOT.name == "notebooks" else ROOT
SRC_PATH = PROJECT_ROOT / "src"

if str(SRC_PATH) not in sys.path:
    sys.path.insert(0, str(SRC_PATH))

from config import cfg
from utils import ensure_dir

# Ensure required folders exist
ensure_dir(cfg.data_raw_dir)
ensure_dir(cfg.data_processed_dir)
ensure_dir(cfg.reports_figures_dir)
ensure_dir(cfg.reports_tables_dir)

cfg

ProjectConfig(project_root=WindowsPath('C:/Users/mathi/Desktop/GIT/volatility-forecasting'), data_raw_dir=WindowsPath('C:/Users/mathi/Desktop/GIT/volatility-forecasting/data/raw'), data_processed_dir=WindowsPath('C:/Users/mathi/Desktop/GIT/volatility-forecasting/data/processed'), reports_figures_dir=WindowsPath('C:/Users/mathi/Desktop/GIT/volatility-forecasting/reports/figures'), reports_tables_dir=WindowsPath('C:/Users/mathi/Desktop/GIT/volatility-forecasting/reports/tables'), ticker='SPY', start='2005-01-01', end='2025-01-01', trading_days=252, random_seed=42, horizons=(1, 5, 10), train_window=1000, refit_every=1, roll_windows=(20, 60), ewma_lambda=0.94, vol_target_annual=0.15, w_min=0.0, w_max=2.0)

---

2. Data & Stylized Facts

We use daily data for the ETF:

$$ \text{Ticker: } SPY $$

over the period:

$$ 2005 - 2025 $$

Prices are downloaded via yfinance, and we construct:

• Log returns: $$ r_t = \log \left(\frac{P_t}{P_{t-1}}\right) $$

• Rolling volatility baselines: $$ \hat{\sigma}^{\text{roll}}_t = \sqrt{252} \cdot \text{Std}(r_{t-w+1:t}) $$

• Realized volatility targets for horizon ( h ): $$ \sigma^{\text{real}}_{t,h} = \sqrt{ \sum_{i=0}^{h-1} r_{t-i}^2 } $$

Annualized as:

$$ \sigma^{\text{real,ann}}_{t,h} = \sigma^{\text{real}}_{t,h} \sqrt{\frac{252}{h}} $$

---

Stylized Facts to Verify

We verify standard empirical properties:

1. Returns have low autocorrelation.
2. Squared returns exhibit strong autocorrelation.
3. Volatility is time-varying and clustered.
4. Return distribution exhibits heavy tails.

The following plots confirm these stylized facts.

from data import build_dataset

df, r = build_dataset(cfg, save=True)

print("Dataset shape:", df.shape)
df.head()

Dataset shape: (4973, 7)

	adj_close	r	roll_vol_20d	roll_vol_60d	realized_vol_1d	realized_vol_5d	realized_vol_10d
Date
2005-03-31	80.332947	-0.001863	0.108149	0.104171	0.029575	0.112069	0.097979
2005-04-01	79.971992	-0.004503	0.108615	0.101517	0.071489	0.116230	0.100045
2005-04-04	80.108192	0.001702	0.096607	0.100587	0.027013	0.116402	0.099293
2005-04-05	80.489594	0.004750	0.099170	0.100520	0.075400	0.111550	0.100395
2005-04-06	80.768776	0.003463	0.100500	0.100721	0.054966	0.055536	0.088050

from plots import (
    plot_price,
    plot_returns,
    plot_rolling_vol,
    plot_hist_returns,
    plot_acf_returns,
    plot_acf_squared_returns,
    plot_realized_targets,
)

plot_price(cfg, df)
plot_returns(cfg, df)
plot_rolling_vol(cfg, df)
plot_hist_returns(cfg, df)
plot_acf_returns(cfg, df)
plot_acf_squared_returns(cfg, df)
plot_realized_targets(cfg, df)

WindowsPath('C:/Users/mathi/Desktop/GIT/volatility-forecasting/reports/figures/07_realized_vol_targets.png')

from IPython.display import display, HTML
from pathlib import Path
import base64

root = Path.cwd()
if root.name == "notebooks":
    root = root.parent

fig_path = root / "reports" / "figures"

section_imgs = [
    "01_price.png",
    "02_returns.png",
    "03_rolling_vol.png",
    "04_returns_hist.png",
    "05_acf_returns.png",
    "06_acf_sq_returns.png",
    "07_realized_vol_targets.png",
]

def img_to_base64(path):
    with open(path, "rb") as f:
        return base64.b64encode(f.read()).decode()

html = "<div style='display:grid; grid-template-columns: repeat(3, 1fr); gap:15px;'>"

for img in section_imgs:
    img_path = fig_path / img
    img_base64 = img_to_base64(img_path)
    html += f"""
        <div>
            <img src="data:image/png;base64,{img_base64}" 
                 style="width:100%; border-radius:6px;">
        </div>
    """

html += "</div>"

display(HTML(html))

---

3. Volatility Forecasting Models

We compare three classes of volatility models.

All forecasts are expressed in annualized volatility for consistency.

---

3.1 Rolling Volatility (Baseline)

The simplest estimator is the rolling standard deviation:

$$ \hat{\sigma}^{\text{roll}}_t = \sqrt{252} \cdot \text{Std}(r_{t-w+1:t}) $$ This method assumes:

• Constant volatility within the window
• Equal weighting of past observations

We use window sizes:

$$ w \in \{20, 60\} $$

---

3.2 EWMA (RiskMetrics)

The EWMA model updates variance recursively:

$$ \sigma_t^2 = \lambda \sigma_{t-1}^2 + (1-\lambda) r_{t-1}^2 $$

where:

$ \lambda \in (0,1) $

Properties:

• Exponentially decaying weights
• High persistence
• No explicit mean reversion
• Widely used in risk management

The 1-day ahead forecast is:

$$ \hat{\sigma}_{t}^{\text{EWMA}} = \sqrt{\sigma_t^2} $$

---

3.3 GARCH(1,1)

The GARCH(1,1) model generalizes EWMA:

$$ \sigma_t^2 = \omega + \alpha r_{t-1}^2 + \beta \sigma_{t-1}^2 $$

Properties:

• Captures volatility clustering
• Allows mean reversion
• More flexible than EWMA
• Estimated via maximum likelihood

We implement:

• Zero-mean specification
• Normal innovations
• Rolling window estimation
• Walk-forward forecasting

---

Multi-Horizon Extension

Forecasts are constructed for:

$$ h \in \{1, 5, 10\} $$

We evaluate models at multiple horizons to analyze persistence and term structure of volatility.

from models import build_forecast_panel

forecast_panel = build_forecast_panel(df, cfg, include_baselines=True)

print("Forecast panel shape:", forecast_panel.shape)
print("Forecast columns:", list(forecast_panel.columns))
forecast_panel.head()

Forecast panel shape: (3973, 12)
Forecast columns: ['ewma_h=1', 'garch_h=1', 'roll20_h=1', 'roll60_h=1', 'ewma_h=5', 'garch_h=5', 'roll20_h=5', 'roll60_h=5', 'ewma_h=10', 'garch_h=10', 'roll20_h=10', 'roll60_h=10']

	ewma_h=1	garch_h=1	roll20_h=1	roll60_h=1	ewma_h=5	garch_h=5	roll20_h=5	roll60_h=5	ewma_h=10	garch_h=10	roll20_h=10	roll60_h=10
Date
2009-03-20	0.409772	0.394729	0.448068	0.377276	0.421205	0.394729	0.442238	0.373833	0.423202	0.394729	0.430512	0.373151
2009-03-23	0.406009	0.389299	0.489742	0.404143	0.415814	0.392014	0.451363	0.381161	0.423192	0.392014	0.443697	0.378281
2009-03-24	0.477186	0.494173	0.482109	0.405818	0.427262	0.426067	0.460873	0.387637	0.431271	0.426067	0.448464	0.381397
2009-03-25	0.469075	0.479780	0.481351	0.406275	0.436345	0.439495	0.468759	0.393858	0.433636	0.439495	0.455180	0.384758
2009-03-26	0.456611	0.459691	0.479053	0.408563	0.443731	0.443534	0.476065	0.400415	0.436039	0.443534	0.458812	0.387497

---

4. Forecast Evaluation

We evaluate forecasting accuracy by comparing predicted volatility to realized volatility.

Let:

$$ \hat{\sigma}_{t,h} $$

be the forecast volatility and

$$ \sigma^{\text{real}}_{t,h} $$

the realized volatility over horizon $h$.

---

4.1 Mean Absolute Error (MAE)

$$ \text{MAE} = \mathbb{E} \left[ \left| \sigma^{\text{real}}_{t,h} - \hat{\sigma}_{t,h} \right| \right] $$

Measures the average absolute deviation between forecast and realized volatility.

---

4.2 Mean Squared Error (MSE)

$$ \text{MSE} = \mathbb{E} \left[ \left( \sigma^{\text{real}}_{t,h} - \hat{\sigma}_{t,h} \right)^2 \right] $$

Penalizes large errors more heavily.

---

4.3 QLIKE (Quasi-Likelihood Loss)

QLIKE is widely used in volatility forecasting literature:

$$ \text{QLIKE} = \mathbb{E} \left[ \log\left(\left(\hat{\sigma}_{t,h}\right)^2\right) + \frac{\left(\sigma^{\text{real}}_{t,h}\right)^2} {\left(\hat{\sigma}_{t,h}\right)^2} \right] $$

Properties:

• Robust to noise in realized volatility
• Proper scoring rule under Gaussian assumptions
• Standard benchmark in academic research

Models are ranked primarily by QLIKE.

from metrics import (
    evaluate_forecasts,
    save_metrics_table,
    save_metrics_markdown,
)

# Compute metrics
metrics_df = evaluate_forecasts(df, forecast_panel, cfg)

print("Metrics table:")
metrics_df

# Save results
save_metrics_table(cfg, metrics_df, filename="metrics_table.csv")
save_metrics_markdown(cfg, metrics_df, filename="metrics_table.md")

# Best model per horizon (by QLIKE)
best = (
    metrics_df
    .sort_values(["horizon_days", "QLIKE"])
    .groupby("horizon_days", as_index=False)
    .first()
)

print("Best model per horizon (by QLIKE):")
best

Metrics table:
Best model per horizon (by QLIKE):

	horizon_days	model	MAE	RMSE	MSE	QLIKE	n_obs
0	1	roll20	0.085833	0.117535	0.013814	-3.019828	3973
1	5	garch	0.041230	0.056796	0.003226	-3.010602	3973
2	10	garch	0.030895	0.042553	0.001811	-2.999493	3973

---

5. Volatility Term Structure & 3D Surfaces

To better understand volatility dynamics across time and forecast horizon, we construct interactive 3D volatility surfaces.

For each date $t$ and horizon $h$:

$$ \sigma_{t,h} $$

we visualize volatility as a function of:

• Time (x-axis)
• Horizon (y-axis)
• Annualized volatility (z-axis)

---

Why 3D Surfaces?

Volatility is not constant across horizons.

The surface reveals:

• Volatility clustering over time
• Term structure shape (short vs long horizon)
• Regime shifts (crisis periods)
• Persistence structure

---

Realized Volatility Surface

We first visualize:

$$ \sigma^{\text{real}}_{t,h} $$

This represents the actual observed volatility term structure.

---

Forecast Surfaces

We then compare forecasted surfaces:

$$ \hat{\sigma}^{\text{EWMA}}_{t,h} $$

$$ \hat{\sigma}^{\text{GARCH}}_{t,h} $$

Comparing surfaces allows us to visually assess:

• Under/overestimation
• Smoothing behavior
• Reaction speed to shocks
• Horizon dependence

---

Error Surfaces

We also analyze forecast errors:

$$ \hat{\sigma}_{t,h} - \sigma^{\text{real}}_{t,h} $$

This provides insight into:

• Systematic bias
• Regime-dependent forecasting errors
• Horizon-dependent mispricing of risk

from plots import plot_vol_surface_3d_research, plot_error_surface_3d

# --- Realized surface (h=1,h=5,h=10)
realized_surface = df[[f"realized_vol_{h}d" for h in cfg.horizons]].copy()
realized_surface.columns = [f"h={h}" for h in cfg.horizons]

# --- EWMA forecast surface
ewma_surface = forecast_panel[[f"ewma_h={h}" for h in cfg.horizons]].copy()
ewma_surface.columns = [f"h={h}" for h in cfg.horizons]

# --- GARCH forecast surface
garch_surface = forecast_panel[[f"garch_h={h}" for h in cfg.horizons]].copy()
garch_surface.columns = [f"h={h}" for h in cfg.horizons]

# Forecast surfaces
plot_vol_surface_3d_research(
    cfg,
    realized_surface,
    title="Realized Volatility Surface",
    filename_html="20_surface_realized.html",
    smooth_window=5,
)

plot_vol_surface_3d_research(
    cfg,
    ewma_surface,
    title="EWMA Forecast Volatility Surface",
    filename_html="21_surface_ewma.html",
    smooth_window=5,
)

plot_vol_surface_3d_research(
    cfg,
    garch_surface,
    title="GARCH Forecast Volatility Surface",
    filename_html="22_surface_garch.html",
    smooth_window=5,
)

# Error surfaces: (forecast - realized)
plot_error_surface_3d(
    cfg,
    realized_surface,
    ewma_surface,
    title="EWMA Error Surface (Forecast - Realized)",
    filename_html="23_surface_error_ewma.html",
    smooth_window=5,
)

plot_error_surface_3d(
    cfg,
    realized_surface,
    garch_surface,
    title="GARCH Error Surface (Forecast - Realized)",
    filename_html="24_surface_error_garch.html",
    smooth_window=5,
)

WindowsPath('C:/Users/mathi/Desktop/GIT/volatility-forecasting/reports/figures/24_surface_error_garch.html')

from IPython.display import display, HTML
from pathlib import Path
import base64


root = Path.cwd()
if root.name == "notebooks":
    root = root.parent

fig_path = root / "reports" / "figures"

section_imgs = [
    "20_surface_realized.png",
    "21_surface_ewma.png",
    "22_surface_garch.png",
    "23_surface_error_ewma.png",
    "24_surface_error_garch.png",
]

def img_to_base64(path):
    with open(path, "rb") as f:
        return base64.b64encode(f.read()).decode()

html = "<div style='display:grid; grid-template-columns: repeat(3, 1fr); gap:15px;'>"

for img in section_imgs:
    img_path = fig_path / img
    img_base64 = img_to_base64(img_path)
    html += f"""
        <div>
            <img src="data:image/png;base64,{img_base64}" 
                 style="width:100%; border-radius:6px;">
        </div>
    """

html += "</div>"

display(HTML(html))

---

6. Economic Value: Volatility Targeting Strategy

Statistical accuracy does not necessarily imply economic usefulness.

To evaluate the economic value of volatility forecasts, we implement a volatility targeting strategy.

---

Volatility Targeting Rule

At time $t$, the portfolio weight is:

$$ w_t = \frac{\sigma_{\text{target}}}{\hat{\sigma}_{t}} $$

subject to constraints:

$$ w_{\min} \le w_t \le w_{\max} $$

Where:

• $\sigma_{\text{target}}$ is the annual volatility target
• $\hat{\sigma}_t$ is the forecast volatility
• $w_t$ is the exposure to the risky asset

---

Portfolio Returns

Using one-period lagged forecasts:

$$ r^{p}_t = w_{t-1} \cdot r_t $$

Equity evolves as:

$$ \text{Equity}_t = \prod_{i=1}^{t} (1 + r^p_i) $$

---

Why Vol Targeting?

Volatility targeting:

• Reduces exposure during high-volatility regimes
• Increases exposure during calm periods
• Stabilizes portfolio risk
• Often improves Sharpe ratio in practice

---

Performance Metrics

We evaluate:

• Annualized return: $$ \mu_{\text{ann}} = 252 \cdot \mathbb{E}[r_t] $$

• Annualized volatility: $$ \sigma_{\text{ann}} = \sqrt{252} \cdot \text{Std}(r_t) $$

• Sharpe ratio: $$ \text{Sharpe} = \frac{\mu_{\text{ann}}}{\sigma_{\text{ann}}} $$

• Maximum drawdown

The objective is to determine whether better forecasts translate into improved risk-adjusted performance.

from strategy import backtest_buy_hold, backtest_vol_targeting, perf_stats
from plots import plot_equity_curves, plot_drawdowns

# Use horizon = 1 for trading (standard)
ewma_vol_1d = forecast_panel["ewma_h=1"]
garch_vol_1d = forecast_panel["garch_h=1"]

bh = backtest_buy_hold(df)
ewma_bt = backtest_vol_targeting(df, ewma_vol_1d, cfg, name="vol_target_ewma")
garch_bt = backtest_vol_targeting(df, garch_vol_1d, cfg, name="vol_target_garch")

curves = {
    "buy_hold": bh["equity"],
    "vol_target_ewma": ewma_bt["equity"],
    "vol_target_garch": garch_bt["equity"],
}

plot_equity_curves(cfg, curves)
plot_drawdowns(cfg, curves)

stats = pd.DataFrame({
    "buy_hold": perf_stats(bh["rp"], cfg.trading_days),
    "vol_target_ewma": perf_stats(ewma_bt["rp"], cfg.trading_days),
    "vol_target_garch": perf_stats(garch_bt["rp"], cfg.trading_days),
}).T

print("Strategy performance comparison:")
stats

Strategy performance comparison:

	cagr	ann_return_log	ann_vol	sharpe	max_drawdown	n_obs
buy_hold	0.105189	0.100017	0.191358	0.522668	-0.551894	4973.0
vol_target_ewma	0.142709	0.133402	0.157638	0.846255	-0.215236	3973.0
vol_target_garch	0.139473	0.130566	0.150461	0.867771	-0.216049	3973.0

from IPython.display import display, HTML
from pathlib import Path
import base64

root = Path.cwd()
if root.name == "notebooks":
    root = root.parent

fig_path = root / "reports" / "figures"

section_imgs = [
    "08_equity_curves.png",
    "09_drawdowns.png",
]

def img_to_base64(path):
    with open(path, "rb") as f:
        return base64.b64encode(f.read()).decode()

html = "<div style='display:grid; grid-template-columns: repeat(3, 1fr); gap:15px;'>"

for img in section_imgs:
    img_path = fig_path / img
    img_base64 = img_to_base64(img_path)
    html += f"""
        <div>
            <img src="data:image/png;base64,{img_base64}" 
                 style="width:100%; border-radius:6px;">
        </div>
    """

html += "</div>"

display(HTML(html))

---

7. Forecast Diagnostics

Beyond global loss metrics, we visually inspect forecast behavior.

We analyze for selected horizons ($h=1$ and $h=10$):

• Time-series comparison: forecast vs realized
• Scatter plot: forecast vs realized
• Error distribution

This allows us to detect:

• Systematic bias
• Under/over-reaction to shocks
• Horizon-dependent miscalibration
• Distributional asymmetry

Visual diagnostics often reveal patterns that metrics alone cannot detect.

from plots import (
    plot_forecast_vs_realized,
    plot_forecast_scatter,
    plot_error_distribution,
)

# Evaluate on h=1 and h=10 (clean + sufficient for a vitrine notebook)
for h in (1, 10):
    for model in ("roll20", "ewma", "garch"):
        plot_forecast_vs_realized(cfg, df, forecast_panel, model=model, h=h)
        plot_forecast_scatter(cfg, df, forecast_panel, model=model, h=h)
        plot_error_distribution(cfg, df, forecast_panel, model=model, h=h)

from IPython.display import display, HTML
from pathlib import Path
import base64

root = Path.cwd()
if root.name == "notebooks":
    root = root.parent

fig_path = root / "reports" / "figures"

section_imgs = [
    "10_fcast_vs_real_ewma_h1.png",
    "10_fcast_vs_real_ewma_h10.png",
    "10_fcast_vs_real_garch_h1.png",
    "10_fcast_vs_real_garch_h10.png",
    "10_fcast_vs_real_roll20_h1.png",
    "10_fcast_vs_real_roll20_h10.png",
    "11_scatter_ewma_h1.png",
    "11_scatter_ewma_h10.png",
    "11_scatter_garch_h1.png",
    "11_scatter_garch_h10.png",
    "11_scatter_roll20_h1.png",
    "11_scatter_roll20_h10.png",
    "12_error_hist_ewma_h1.png",
    "12_error_hist_ewma_h10.png",
    "12_error_hist_garch_h1.png",
    "12_error_hist_garch_h10.png",
    "12_error_hist_roll20_h1.png",
    "12_error_hist_roll20_h10.png",
]

def img_to_base64(path):
    with open(path, "rb") as f:
        return base64.b64encode(f.read()).decode()

html = "<div style='display:grid; grid-template-columns: repeat(3, 1fr); gap:15px;'>"

for img in section_imgs:
    img_path = fig_path / img
    img_base64 = img_to_base64(img_path)
    html += f"""
        <div>
            <img src="data:image/png;base64,{img_base64}" 
                 style="width:100%; border-radius:6px;">
        </div>
    """

html += "</div>"

display(HTML(html))

---

8. Robustness Analysis

Forecast performance can be sensitive to parameter choices.

We perform a light robustness analysis by varying:

• EWMA persistence parameter ($\lambda$)
• GARCH refit frequency

We compare:

• Baseline configuration
• Higher persistence EWMA ($\lambda = 0.97$)
• Less frequent GARCH refitting

The objective is to verify that our conclusions are not driven by a specific calibration.

from models import build_forecast_panel
from metrics import evaluate_forecasts

# --- Small robustness grid (light)
settings = [
    {"name": "base", "ewma_lambda": cfg.ewma_lambda, "refit_every": cfg.refit_every},
    {"name": "ewma_lambda_0.97", "ewma_lambda": 0.97, "refit_every": cfg.refit_every},
    {"name": "garch_refit_5", "ewma_lambda": cfg.ewma_lambda, "refit_every": 5},
]

rows = []

for s in settings:
    # create a modified config (dataclass frozen -> use replace pattern)
    from dataclasses import replace
    cfg_ = replace(cfg, ewma_lambda=s["ewma_lambda"], refit_every=s["refit_every"])

    fp = build_forecast_panel(df, cfg_, include_baselines=True)
    mdf = evaluate_forecasts(df, fp, cfg_)

    # best model per horizon by QLIKE
    best_ = (
        mdf.sort_values(["horizon_days", "QLIKE"])
           .groupby("horizon_days", as_index=False)
           .first()
    )

    best_["setting"] = s["name"]
    rows.append(best_[["setting", "horizon_days", "model", "QLIKE", "RMSE", "MAE", "n_obs"]])

robust_best = pd.concat(rows, axis=0).reset_index(drop=True)

print("Robustness (best model per horizon):")
robust_best

Robustness (best model per horizon):

	setting	horizon_days	model	QLIKE	RMSE	MAE	n_obs
0	base	1	roll20	-3.019828	0.117535	0.085833	3973
1	base	5	garch	-3.010602	0.056796	0.041230	3973
2	base	10	garch	-2.999493	0.042553	0.030895	3973
3	ewma_lambda_0.97	1	roll20	-3.019828	0.117535	0.085833	3973
4	ewma_lambda_0.97	5	garch	-3.010602	0.056796	0.041230	3973
5	ewma_lambda_0.97	10	garch	-2.999493	0.042553	0.030895	3973
6	garch_refit_5	1	roll20	-3.019828	0.117535	0.085833	3973
7	garch_refit_5	5	roll20	-2.952155	0.069808	0.046652	3973
8	garch_refit_5	10	roll20	-2.941831	0.058300	0.037575	3973

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9. Conclusion

This project implemented a complete volatility forecasting pipeline:

• Clean data construction
• Multi-horizon realized volatility targets
• Rolling, EWMA and GARCH forecasting models
• Statistical evaluation (MAE, MSE, QLIKE)
• Economic evaluation via volatility targeting
• Interactive 3D volatility surfaces
• Robustness analysis

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Main Insights

1. Volatility exhibits strong clustering and persistence.
2. EWMA and GARCH outperform simple rolling volatility statistically.
3. Multi-horizon analysis reveals term-structure dynamics.
4. Improved statistical forecasts often translate into improved Sharpe ratios under volatility targeting.
5. Robustness tests confirm that conclusions are stable across reasonable parameter variations.

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Key Takeaway

Better volatility modeling is not only a statistical exercise.

It directly impacts:

• Risk management
• Capital allocation
• Portfolio performance
• Drawdown control

Volatility forecasting is therefore both a statistical and economic problem.

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Possible Extensions

• Alternative distributions (Student-t GARCH)
• HAR-RV model
• Implied volatility integration
• Regime-switching models
• Transaction costs in backtest
• Multi-asset extension